Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping

The inclusion of cognitive processes, such as perception, learning and memory, are inevitable in mechanistic animal movement modelling. Cognition is the unique feature that distinguishes animal movement from mere particle movement in chemistry or physics. Hence, it is essential to incorporate such knowledge-based processes into animal movement models. Here, we summarize popular deterministic mathematical models derived from first principles that begin to incorporate such influences on movement behaviour mechanisms. Most generally, these models take the form of nonlocal reaction-diffusion-advection equations, where the nonlocality may appear in the spatial domain, the temporal domain, or both. Mathematical rules of thumb are provided to judge the model rationality, to aid in model development or interpretation, and to streamline an understanding of the range of difficulty in possible model conceptions. To emphasize the importance of biological conclusions drawn from these models, we briefly present available mathematical techniques and introduce some existing "measures of success" to compare and contrast the possible predictions and outcomes. Throughout the review, we propose a large number of open problems relevant to this relatively new area, ranging from precise technical mathematical challenges, to more broad conceptual challenges at the cross-section between mathematics and ecology. This review paper is expected to act as a synthesis of existing efforts while also pushing the boundaries of current modelling perspectives to better understand the influence of cognitive movement mechanisms on movement behaviours and space use outcomes.

Viewing animal migration through a social lens

Evidence of social learning is growing across the animal kingdom. Researchers have long hypothesized that social interactions play a key role in many animal migrations, but strong empirical support is scarce except in a few unique systems and species. In this review, we aim to catalyze advances in the study of social migrations by synthesizing research across disciplines and providing a framework for understanding when, how, and why social influences shape the decisions animals make during migration. Integrating research across the fields of social learning and migration ecology will advance our understanding of the complex behavioral phenomena of animal migration and help to inform conservation of animal migrations in a changing world.